Method for the transmission of a signal

ABSTRACT

The process disclosed enables the &#34;time domain aliasing cancellation&#34; method to be extended systematically to larger block overlapping. The boundary conditions which, when using various modified transforms, the analysis and synthesis windows must comply with, can thus be given. The transform series must also be included in the design of each analysis and synthesis window in order to optimize for a given application, because this changes the boundry conditions with which an analysis window function can be determined. Design for analysis and synthesis windows have shown that analysis and synthesis properties obtained by multiple block overlapping are significantly better than those obtained by convential double block overlapping. The systematic method of the invention offers numerous possibilites for optimizing windows in special applications.

BACKGROUND OF THE INVENTION

This invention is directed to a method of transmitting a signal usingdigital compression techniques. In the transmission of an audio signal,for example, radio broadcast transmission, cable transmission, satellitetransmission and with recording devices the analog signal is convertedinto a digital signal with a certain resolution, transmitted in digitalform and reconverted into an analog signal upon reception. A greatersignal-to-noise ratio is achieved, in particular upon reproduction, byusing digital transmission.

The band width required for the transmission of such a signal isessentially determined by the number of [scanning values] samples pertime unit which are to be transmitted. The resolution is also a functionof the number of [scanning values] samples transmitted.

In practice it is preferable to keep the transmission band width asnarrow as possible in order to be able to transmit as many audio signalsas possible simultaneously via a wide band channel. It would appear thatthe necessary band width can be reduced by decreasing the number of[scanning values] samples or the number of bits per [scanning value]sample. However, in general this measure results in a deterioration inthe quality of the reproduction.

A method described in DE-OS 35 06 912, improves the quality of thereproduction by separating the digital audio signal into successivetemporal segments and transforming the audio into a short-time spectrumwhich represents the spectral components of the signal for therespective time segments. Generally, in the short-time spectrum, forreasons of psychoacoustic laws, components which are not perceived bythe listener, i.e., are irrelevant from a communications technologyviewpoint, can be discovered more readily than in the time domain. Upontransmission these components are given less weight or are left outentirely. In doing this a considerable part of the otherwise necessarydata can be left out so that the average bit rate can be considerablyreduced.

To form the time segments, the signal is first evaluated in the temporalregion (time domain) using an analysis window and after transformation,coding, transmission, decoding and inverse transformation, is finallyevaluated using a synthesis window. The design of the analysis windowinfluences the frequency resolution. The advantage of a high frequencyresolution is that with narrow band signal components only a smallamount of data is required for their coding, thereby achieving a veryeffective bit allocation, and the average data quantity which is neededfor transmission is considerably reduced. Therefore, for windows with"hard" edges, such as exhibited by a rectangle, the frequency resolutionis poor. This is because the spectral components caused by the extremerise and fall of the signal at the start and end of the window are addedto the spectrum of the original signal in the evaluated segment.However, the temporal segments can be joined to each other withoutoverlaps.

With the method described in DE-OS 35 06 912, a window function with"softer" edges was already selected. Here, the start and the end of theanalysis window follow a cosine [square] function and the correspondingregions of the synthesis window a sine [square] function. The centralarea of both windows has a constant value. The use of such a windowfunction design results in an improved frequency resolution. However, inthe region of the "soft" edges overlapping of the successive temporalsegments is necessary, and this leads to an increase in the average bitrate due to the doubled transmission of the signals contained in thisregion.

A further improvement in the frequency resolution could be achieved byusing an even lower edge gradient for the window function of theanalysis window as well as by expanding the edge region within thewindow. However, with these measures increased overlapping withneighboring temporal segments is required.

If the edge region is expanded so far that the window functions nolonger have a constant value in any region, then adjacent temporalsegments must overlap each other by 50 per cent. This means that thenumber of [scanning values] samples and, accordingly the quantity ofdata, is doubled.

From the publication of J. P. Pfineen and A. B. Bradley"Analysis/Synthesis Filter Bank Design Based on Time Domain AliasingCancellation", IEEE Transactions, ASSP-34, No. 5, October 1986, pp. 1153through 1161, and that of J. P. Princen, A. W. Johnson and A. B. Bradley"Suband/Transform Coding Using Filter Bank Design Based on Time DomainAliasing Cancellation", IEEE Int. Conference on Acoustics, Speech andSignal Processing 1987, pp. 2161 through 2164, it is known with a 50 percent overlap of successive temporal segments to reduce the quantity ofdata to the original value again, in that only every second [scanningvalue] sample is encoded. In the spatial domain every sample is encoded(if data reduction is not considered). Sub-sampling is performed in thespectral domain. The sub-sampling process is explained at page 1154 and1155 of the Princen and Bradley reference noted above. This proposal isbased on equal window functions for the analysis and synthesis windows.In the case of equal window functions, the aliasing components whichappear upon [sub-scanning (]sub-sampling[)] can be compensated for bythe synthesis window after the evaluation.

It was discovered that the frequency resolution can be raised byselecting larger overlapping regions if, at the same time, the signal isassessed with suitable analysis and synthesis windows. In order toreduce the climbing data rate, caused by the higher number of [scanningvalues] samples, to the original value, the sub-[scanning] would have tobe performed using an even higher factor, whereby however, furtheraliasing components ensue.

SUMMARY OF THE INVENTION

It is the object of the invention to specify measures for a method forthe transmission of a signal, whereby said measures are generallyapplicable and also enable, with multiple overlapping blocks, areduction in the number of [scanning values] samples and, therewith, inthe data rate with simultaneous compensation of the aliasing componentscaused by sampling in the frequency domain. Compensation of suchaliasing is achieved by arranging aliasing Components SO as to cancelduring inverse processing at a receiver.

The method makes it possible to specify the general conditions for thetransformations of overlaps which correspond to a power of two, i.e.,for a double, quadruple, eightfold overlap, etc., and to utilize thesewith a practical arrangement. Further developments of the method providefor also determining the general conditions for various analysis andsynthesis windows and using these in practical application.

Through applying the procedure steps according to the invention it ispossible to take advantage of the analysis characteristics of softeranalysis window functions improving with increasing overlapping. Throughcorresponding sub-[scanning] sampling in the [frequency range (frequencydomain)] frequency domain, the effort required for multiple transmissionof partial window regions is reduced to the original data rate of the[temporal] time domain signal.

Data reduction (based on the input data rate) can be achieved usingknown methods, for example as described in DE-OS 3506912. It is hereinrecognized that if overlapping windows are required for coding, theoutput data rate would increase in relation to the amount ofoverlapping. In accordance with the principles of the present inventionthere is disclosed herein a system for significantly reducing orsubstantially avoiding such a data rate increase, particularly in thecase of a significant amount of overlapping, thereby maintaining highsignal quality.

[In the drawings:]

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow diagram with the main procedure steps of the invention

FIG. 2 shows a graphic representation of the segmentation of thecontinuous temporal signal,

FIG. 3 is a block formation from the segmented original signal,

FIG. 4 shows an even and an odd block signal component,

FIG. 5 shows a periodized even block signal component,

FIG. 6 shows [a] sub-[scanning] in the [spectrum] frequency domain bythe factor 2 and offset to the coordinates origin of TB/2 in the timedomain with cosine transformation,

FIG. 7 shows sub-[scanning] sampling in the spectrum by the factor 2 andoffset to the coordinates origin of TB/4 in the time domain with cosinetransformation,

FIG. 8 shows signal components in the case of overlapping summation forvarious offsets of the block start to the coordinates origin,

FIG. 9 shows sub-[scanning] sampling in the spectrum by the factor 2,offset to the coordinates origin of TB/4 in the time domain, and offsetby half a [scanning] sampling period in the case of scanning in thefrequency domain with cosine transformation,

FIG. 10 shows signal components after transformation, sub-[scanning]sampling transmission and inverse transformation for varioustransformations,

FIG. 11 shows signal reconstruction with 50 per cent overlap,

FIG. 12 shows segmentation of analysis and synthesis windows,

FIG. 13 shows components of the analysis and synthesis windows in therespective block region,

FIG. 14 shows signal components after transformation, sub-[scanning]sampling, transmission and inverse transformation in the synthesiswindow region for various transformations with quadruple blockoverlapping,

FIG. 15 shows aliasing compensation with rectangular window for analysisand synthesis,

FIG. 16 shows a compensation scheme for the alternating application ofsine and cosine transformation,

FIG. 17 shows double overlap in the time domain,

FIG. 18 shows quadruple overlap in the time domain,

FIG. 19 shows eightfold overlap in the time domain,

FIG. 20 shows double overlap in the frequency domain,

FIG. 21 shows quadruple overlap in the frequency domain,.

FIG. 22 shows eightfold overlap in the frequency domain.

FIG. 23 is an amplitude vs. frequency plot of spectral lines of ashort-time frequency spectrum.

FIGS. 24A-C show waveforms associated with the processing of a suddenacoustic event.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 shows the method steps according to the invention. Steps 7-12include operations which are the inverse of operations performed insteps 1-7. Briefly, after analog-to-digital conversion in step 1, insteps 2 and 3 overlapping blocks each having groups of a fixed number of1024 values are selected and subjected to a window analysis in step 4.After window analysis the values of each block are processed by steps 5and 6 before coding and transmission in step 7. This processing includesfrequency transformation which produces transform output values. Thetransform output values are sampled or subsampled, causing aliasing. Thesampled transform output values are arranged so that aliasing occurs atcertain positions which result in aliasing being cancelled as a resultof inverse processing e.g., at a receiver. The coding in step 7 may takethe form of any well known data reduction technique, with the decodingin step 7 being the inverse of the coding technique used.

In the flow diagram illustrated in FIG. 1, the individual proceduresteps for executing the method of the invention are shown. The [statingvariable] source signal of the method forms an analog audio signal whichis converted according to procedure step 1 into a digital signal, inwhich amplitude values are present as [scanning values ] samples indigital coded form. In procedure step 2 the continuous signal iswindowed, in that a series of successive [scanning values] samples, inthe ease presented here, 1024 [scanning values] samples, are selected.For example, a 1024 bit serial-to-parallel register can be used forreceiving the continuous input sample data stream and outputting groupsof 1024 samples.

In procedure step 3 blocks with temporal overlaps of 50 per cent areformed from the selected [scanning values] samples. This means that inadjacent blocks sometimes the same [scanning values] samples arepresent, albeit in different places. Thus, the [scanning values] samplespresent in the first half of a current block correspond to the [scanningvalues] samples present in the second half of the preceding block. Thesamples satisfy the Shannon theory. The overlapping is caused by takingthe same sample twice, in the neighboring and overlapping blocks.

In procedure step 4 the signal segments contained in the blocks areevaluated using analysis windows. In doing this a soft signal rise andfall are created at the block boundaries which raises the analysissharpness for the following transformation. Each analysis window isevaluated without regard to overlapping. In the evaluation, 1024 samples(which are known to be used in other windows) are selected andprocessed. This procedure is also used for the subsequent steps oftransformation (5), coding, transmission and decoding (7) and inversetransformation (8).

Procedure step 5 forms the transformation of the existing discrete-timesignal into a discrete-frequency signal. Instead of amplitude values,spectral values appear from now on which each encompass a real and animaginary component. The outputs of a sine or cosine transform are realvalues. If an FFT (Fast Fourier Transform) is used for calculating theoutput values, imaginary components also result.

Next, the conversion of the spectral values into a presentation with[pseudoquantities] pseudo amplitude values and pseudophases takes placein procedure step 6. The spectral values are then prepared and suitedfor a transmission method such as is described in DE-OS 35 06 912.Sub-[scanning] sampling is also performed at the same time in connectionwith the conversion of the spectral values. The result is that thenumber of values to be transmitted again coincides with the number oforiginal [scanning values] samples. The doubling of the data caused bythe 50 per cent overlapping of the blocks is, therefore, cancelled here.

In the procedure step designated 7, several individual steps arecombined encompasses the coding, if applicable the data reduction,transmission and decoding. These procedure steps can be carried outaccording to the method in DE-OS 35 06 912.

Regarding the processing in steps 6 and 7, as discussed in DE-OS3506912, after spectral transformation in step 5 the signal is coded insteps 6 and 7 to produce coding according to psychoacoustic principles.By means of such psychoacoustic coding, spectral components which arenot detected at a reproduction stage, in particular because of maskingeffects, are weighted less strongly or are omitted during the codingprocess. This type of processing of the short-term spectrum may readilybe accomplished, e.g., by means of a computer. FIG. 23, which will bediscussed in detail subsequently, shows the amplitude plot of spectrallines of a short-term frequency spectrum of a signal transform at theoutput of step 5. The signal coded in this manner may be transmitted viaa narrow-band transmission channel due to a reduction in the mean datarate. The transmission channel is followed by a receiver which performsessentially the inverse of the transmitter functions, includingdecoding. An analog signal eventually produced at the output of D/Aconverter 12 is not identical to an input analog signal in step 1,because in the coding process spectral components have been weighteddifferently or suppressed. The difference between such analog signals,however, is not noticed by a listener at the reproduction stage.

In procedure step 8 transformation inverse to that in procedure step 5takes place while, however, with preceding data reduction, the signalsubjected to this is a modified signal freed from psycho-acousticallyredundant components. The result of the inverse transformation is againdiscrete-time signals in the form of blocks representing signal segmentsof a continuous signal. However, only half the original [scanningvalues] samples are present in the blocks.

In procedure step 9, the blocks are weighted with synthesis windows. Thesynthesis window functions are so designed that they again compensatethe signal distortions which have come about as a result of the[weighting] overlapping with the analysis windows in procedure step 4.The synthesis window itself does not compensate for signal distortion,e.g., alias components, but its special location and combination withthe analysis window causes the compensation. The signal distortion(alias components) is caused by the overlapping, not by the weighting.The synthesis window functions used here fulfill two criteria. Firstly,they complement themselves to one in the overlap region using thecorresponding analysis windows. Secondly, the analysis window reflectedin the center of the overlap region multiplied by the synthesis windowfor the block n in the difference with the analysis window reflected inthe center of the overlap region multiplied by the synthesis window forthe block n+1 in the overlap region is identical to zero. This lattercriterion contains the compensation for the aliasing components. Steps 2through 9 are performed serially for each block of 1024 samples. If therequired results (see, for example, FIG. 11) from step 9 are present,the addition function of step 10 can be made, resulting in thecontinuous samples as indicated by step 11 (see, for example, the bottomof FIG. 11).

In procedure step 10 the blocks overlapping by 50 per cent are added,whereby the aliasing components in the two blocks to be superimposedappear with reversed preceding signs so that upon addition itcompensates to zero.

In procedure step 11 the formation of continuous [scanning values]samples through joining the blocks to each other with the windowedsignal segments is illustrated.

Finally, in the last procedure step, designated 12, conversion of thedigital, coded [scanning values] samples into an analog signal iscarried out, whereby, objectively, components are in fact missing butwhich, subjectively, is experienced as identical with the originalsignal.

In the further explanation the cosine or, respectively, the sinetransformation is to serve as the basis of the multiply overlappingtransformations. In addition, temporal continuous signals shall beassumed for all procedure descriptions. The transition to discrete-timesignals can, separately from the further considerations, be carried outaccording to the generally known procedure.

The cosine transformation is defined as an integral transformation fromthe following pair of equations: ##EQU1##

Accordingly, the following applies for the sine transformation: ##EQU2##

The constants Ac, Be, As and Bs serve for normalizing purposes and arenot significant for the further considerations. Corresponding to theequations (1) through (4), the temporal function f(t) for the cosine or,respectively, the sine transformation shall only be different from zerofor the case of t larger than 0. For a transformation with finite blocklength this can always be achieved through suitable selection of thecoordinates origin.

The cosine and sine transformation can be traced back to the Fouriertransformation, in that, for the cosine transformation, the even signalcomponent is fed to a Fourier transformation and, respectively, the oddsignal component for the sine transformation. Using this transfer, alltheorems known for the Fourier transformation can also be utilized forthe sine and cosine transformations.

The continuous [temporal] time domain signal is divided into segmentscorresponding to the block regions which, after transformation,sub-[scanning,] sampling transmission and inverse transformation, arefed to the overlapping summation. If the block length is designated TB,then the segments with 50 per cent overlap have the length TB/2, asshown in FIG. 2. The segments in temporal [sequence] order aredesignated with Ni.

If blocks with 50 per cent overlap are removed from the continuoussignal so described by means of a simple rectangular window, then thereresult, for example, the blocks obvious from FIG. 3 for a cycleconsisting of transformation, sub-[scanning] sampling, transmission andinverse transformation.

If the coordinates origin is so chosen that it coincides with the startof the transformation block, then the even or, respectively, odd signalcomponent of such a transformation block multiplied by the factor 2 is,in this scheme, as shown in FIG. 4.

Here, the reflected signal components corresponding to the signalcomponents Ni are designated Si. The negative sign with an odd signalcomponent indicates that the reflected signal components appear negativein comparison to the corresponding original components.

The scanning of the Fourier transformed variable of the even or oddsignal component leads in the time domain to a periodizing of thecorresponding signal components. If in the time domain no aliasingdisturbance is to ensue, then the periodized signal components are notpermitted to overlap. This means that in the spectrum, a [scanning]sampling period of Fo=1/(2TB) must be used in the borderline case. Thisperiodizing, with the aid of the scheme, for example, for the cosinetransformation, leads to the situation shown in FIG. 5.

One degree of freedom, which until now was relatively arbitrarilyestablished, is the position of the start of the block in the usedcoordinate system of the transformation. Up to now, the start of theblock coincided with the zero point of the coordinate system. A shift inthe start of the block towards positive times t in the coordinate systemand the consequences of a sub-[scanning] sampling by the factor 2 in thespectrum, i.e., a [scanning] sampling period of Fo=1/(2TB), isillustrated in FIGS. 6 and 7 using the example of the cosinetransformation. Shown in FIG. 6 are the various signal components in thetime domain after transformation, [subscanning] subsampling,transmission and inverse transformation with an offset of thetransformation block from the coordinates origin of TB/2. The signalcomponents with an offset of TB/4 are shown in FIG. 7.

From these two examples it can be seen what influence this importantdegree of freedom has on the components located in the region which isblanked out from the periodically repeated signal components using thesynthesis window in the receiver. This time region has the duration TBin both representations and has the position characterized in the twopictures. The region of the synthesis window contains, firstly, theoriginal signal segments N1 and N2 and, secondly, the aliasingcomponents S1 and S2. FIGS. 6 and 7 show that the offset of the start ofthe block from the coordinates origin determines, on the one hand, atwhich point in the block region the signal components resulting fromreflection appear but, on the other hand, has no influence on the signalcomponents with a noninverted temporal position.

As the method of aliasing compensation demands that the aliasingcomponents are compensated through summation of the block overlapregions of the affected blocks, with double overlapping only thosesignal components may be located in one half of a block which originatefrom the same block half in the original signal. This requirement is notfulfilled by a temporal offset and size of TB/2 because here reflectedsignal components from the second half of the block occur in the firsthalf and vice versa. In this case, with a block overlap, n components,originating from the overlap region n-1 as well as n+1, appear in theoverlap region. As these components only appear once in the respectiveoverlap region, they cannot compensate themselves. FIG. 8 shows, forsuccessive blocks, which signal components are basically involved in thesummation in the overlap region for offsets TB/2 and TB/4.

As only a temporal offset of TB/4 contains the basically correctcomponents, in order to, on the one hand, create the wanted signal aftera summation in the overlap region and, on the other hand, to compensatethe aliasing components, this offset of the start of the block from thecoordinates origin is used for the cosine or, respectively, the sinetransformation.

A further degree of freedom is represented by the [scanning] samplingscheme in the frequency domain. Here, it is possible to either let the[scanning] sampling start at the frequency f=0 or, however, to introducea [scanning] sampling offset corresponding to half the [scanning]sampling period during scanning in the frequency domain. Other offsetdimensions lead to a doubling of the data rate through an asymmetric[scanning] sampling of the symmetrical image function for the cosine or,respectively, sine transformation in the Fourier spectral space. Theoffset by half the [scanning] sampling period with the [scanning]sampling in the spectrum effects an alternating change in preceding signwith the periodizing of the even or, respectively, the odd blockcomponent after transformation, sub-[scanning] sampling, transmissionand inverse transformation in the time domain. FIG. 9 illustrates thiswith the scheme used for the cosine transformation.

It can be seen from FIGS. 7 and 9 which signal components for the cosinetransformation after transformation, sub-[scanning] sampling,transmission and inverse transformation are located in the region whichis blanked out with the synthesis window. If it is considered that, withthe sine transformation, only the reflected components have a negativesign with regard to those with the cosine transformation, then, for thisalso, the signal components in the region of the synthesis window can bespecified. In FIG. 10 the signal components located in the region of thesynthesis window after transformation, sub-[scanning] samplingtransmission and inverse transformation are specified for the fourpossible transformation variations: cosine transformation with andwithout [scanning] sampling offset in the spectrum as well as sinetransformation with and without [scanning] sampling offset in thespectrum. In the case of a two-fold overlapping (N=2) of the windows,every Nth (2nd) sample value is omitted, producing two-fold subsamplingin the transform output. In single overlapping (N=1), every value issampled.

The expression "reflected" as used in the preceding description means"mirrored". The mirrored effect arises automatically if values aresamples. e.g., repeat spectra. No special use is made of the mirroredcomponents. The overlapping i.e., the twofold evaluation of the inputsamples, together with a two fold subsampling in the frequency domain,leads to the same number of output samples.

In FIG. 11 the mechanism for the aliasing compensation of severalsuccessive blocks is shown using an offset of TB/4. From the possibletransformation variations, alternating cosine and sine transformationwithout [scanning] sampling offset in the frequency domain is to beapplied here with temporally successive blocks. Thus, one of thealiasing components receives a positive sign and the other componentreceives a negative sign.

In the above-mentioned example, rectangular windows were used asanalysis and synthesis window functions. However, these windows show anextremely poor behavior with respect to selectivity in the spectraldomain. Better results are achieved if window functions with "soft"edges are used for analysis and synthesis.

When using window functions which deviate from the rectangular windowfunction, two conditions must be observed.

1. the wanted signal must be correctly reconstructed by the overlapping;

2. the aliasing disturbance must further be compensated.

In order to be able to set up the equations necessary for maintainingthese two conditions the technique to be used must correspond andsupplement the [tehnicque] technique described above.

When the analysis window and the synthesis window are segmented in thesame way as the signal, then a situation according to that of FIG. 12results. Corresponding to the signal components, the components of theanalysis or, respectively, the synthesis window, present in a temporallyregular arrangement, are now designated with an1 and sn1 respectively.Components of the analysis window, temporally inverted owing to thereflection, are designated asi. If the window segments, which wereinvolved in the reconstruction of the respective signal components, arenow inserted into FIG. 11, then a situation according to that of FIG. 13results. The equations, which must be met by the analysis and synthesisfunctions so that, after the summation in the overlap region, the signalis itself reconstructed on the one hand and the aliasing disturbancesare compensated on the other, can be read off from this representationwith the aid of FIG. 11.

Two equations for the regions of the block overlaps result from FIG. 13:

    an1*sn1+an2*sn2=1 (reconstruction rule)                    (5)

    -as1*sn1+as2*sn2=0 (compensation rule)                     (6)

If with all temporally successive transformations identical windowfunctions are used and if the analysis window functions are designateda(x), where x is a standardized time which has the value 0 at the startof the block and the value 1 at the end of the block, as well as if thesynthesis function is designated with s(x), then using the equations (5)and (6) for the overlap regions 0 less or x less or 0.5 we get:

    a(x)*s+a(x+0.5)*s(x+0.5)=1                                 (7)

    a(0.5-x)*s(x)-a(1-x)*s(0.5+x)=0                            (8)

These two equations must be fulfilled by the window functions. If thespecial case is chosen in which the window functions are symmetricalabout the center of the block and it is assumed that the analysis windowfunction is predetermined, then a construction rule for the synthesiswindow function results from the equations (7) and (8): ##EQU3##

Following this, the method explained through the example of the doubleoverlap will be systematically extended to larger block overlaps, namelythe quadruple and eightfold overlap.

The degrees of freedom, shifting of the block zero point in the temporalcoordinate system and offset with the [scanning] sampling in thespectral region are determined according to the above considerations.This leads to a shifting of the block zero point with respect to thecoordinates origin by one eighth of the block length TB. The offset zeroand the shifting by half a [scanning] sampling period during scanning inthe spectrum are also permitted in this case. Consequently, fourtransformation modifications result from the quadruple block overlap.The signal components located in the region of the synthesis windowafter transformation, sub-[scanning] sampling, transmission and inversetransformation, firstly using rectangular window functions for analysisand synthesis, are shown in FIG. 14 for all valid transformations.Similarly to the case of the double overlap, a segmentation of thesignal was carried out here with the temporal expansion of the commonoverlap region of TB/4.

Under the precondition of the aliasing compensation with the applicationof rectangular windows for analysis and synthesis, there results thefollowing temporal transformation sequence:

1. sine transformation with sub-[scanning] sampling by the factor 4,offset by TB/8 in the time domain and offset by half a [scanning]sampling period with [scanning] sampling in the spectrum;

2. sine transformation with sub-[scanning] sampling by the factor 4,offset by TB/8 in the time domain and no offset with [scanning] samplingin the spectrum;

3. cosine transformation with sub-[scanning] sampling by the factor 4,offset by TB/8 in the time domain and offset by half a [scanning]sampling period with [scanning] sampling in the spectrum;

4. cosine transformation with sub-[scanning] sampling by the factor 4,offset by TB/8 in the time domain and no offset with [scanning] samplingin the spectrum.

When temporal transformation sequence is employed, then, using thescheme already used before, the situation shown in FIG. 15 results.

If we also again perform an appropriate segmentation for analysis andsynthesis windows using the designations an1, as1 and sn1 for theindividual segments in original temporal arrangement and in temporallyinverted arrangement, then we can also specify the equations here whichhave to be generally fulfilled by the window functions:

    an1*sn1+an2*sn2-an3*sn3+an4*sn4=1                          (10)

    as1*sn1+as2*sn2-as3*sn3-as4*sn4=0                          (11)

    an1*sn3=an2*sn4                                            (12)

    an3*sn1=an4*sn2                                            (13)

    as1*sn3=as2*sn4                                            (14)

    as3*sn1=as4*sn2                                            (15)

If, for reasons of simplification, it is again assumed, that the windowfunctions are always functions symmetric about the block center, then aconstructional rule is gained from the equations (12) through (15) whichmust be met by the analysis window. This rule is specified in a formwhereby x again corresponds to the standardized time. It is summarizedin the equations (16) and (17):

    a(0.5-x)*a(x)=a(0.25+x)*a(0.25-x)                          (16)

    a(1-x)*a(x+0.5)=a(0.75+x)*a(0.75-x)                        (17)

for [0</=x</=0.25] 0≦x≦0.25

By specifying an analysis window which meets the rules (16) and (17), acorresponding synthesis window can be calculated using the system ofequations (1*): ##EQU4##

If it is not assumed that an aliasing compensation is to be present withthe application of rectangular windows but, rather, that the aliasingcomponents only compensate when using a certain window function which isdifferent from a rectangular window, then we can deviate from thetemporal transformation sequence specified above and apply any arbitrarytransformation sequence. By using another transformation sequence theequations (10) through (15) alter if necessary and hence theconstructional rules for analysis and synthesis windows. However, as thesignal components with all transformations are the same in the region ofthe synthesis window and are merely differentiated by their precedingsigns, the structure of the equations (10) through (15) with theirsegments of analysis and synthesis windows remains and only the signs inthese six equations alter through a temporally different transformationsequence. However, this means for the constructional rule in equations(16) and (17), which must be met by the analysis window, that here thereare basically only two different rules. Firstly, the one specified inequations (16) and (17); secondly, one with a negative sign on one sideof the equals sign in both equations. As an example of such a case thealternating application of sine and cosine transformation without[scanning] sampling offset in the spectrum is to be specified. FIG. 16illustrates the scheme with this transformation sequence with theprecondition of rectangular windows for analysis and synthesis.

The equations for the analysis and synthesis windows then readaccordingly:

    an1*sn1+an2*sn2+an3*sn3+an4*sn4=1                          (19)

    an1*sn1-as2*sn2+an3*sn3-as4*sn4=0                          (20)

    an1*sn3=-an2*sn4                                           (21)

    an3*sn1=-an4*sn2                                           (22)

    as1*sn3=as2*sn4                                            (23)

    as3*sn1=as4*sn2                                            (24)

and hence the constructional rule for the analysis window:

    a(0.5-x)*a(x)=-a(0.25+x)*a(0.25-x)                         (25)

    a(1-x)*a(x+0.5)=-a(0.75+x)*a(0.75-x)                       (26)

for [0</=x</= or 0.15] 0≦x≦0.15.

The considerations made in conjunction with the quadruple overlap can besystematically transferred to higher degrees of overlapping, forexample, the eightfold overlap. The offset between the start of theblock and the zero point of the coordinate system now has the sizeTB/16. Furthermore, again only the four transformation variations can beused like with the quadruple block overlap. It is also valid that thetemporal transformation sequence only has an influence on the precedingsigns of the signal components, not, however, on their temporal positionin the region of the synthesis window after transformation,sub-[scanning] sampling, transmission and inverse transformation.

Fourteen (14) equations which must be fulfilled by analysis andsynthesis windows result from similar considerations for the followingtransformation sequence:

1. sine transformation with sub-[scanning] sampling by the factor 4,offset by TB/8 in the time domain and offset by half a [scanning]sampling period with [scanning] sampling of the spectrum;

2. sine transformation with sub-[scanning] sampling by the factor 4,offset by TB/8 in the time domain and no offset with [scanning] samplingof the spectrum;

3. cosine transformation with sub-[scanning] sampling by the factor 4,offset by TB/8 in the time domain and offset by half a [scanning]sampling period with [scanning] sampling of the spectrum;

4. cosine transformation with sub-[scanning] sampling by the factor 4,offset by TB/8 in the time domain and no offset with [scanning] samplingof the spectrum;

Three equations, to be understood as conditions to be fulfilled by theanalysis window, can be extracted from this. The conditions are asfollows with the precondition of axis-symmetrical analysis and synthesiswindow functions:

    a(x)*(0.25-x)=a(0.125+x)*a(0.125-x)                        (27)

    a(x)*a(0.5-x)+a(0.125+x)*a(0.375-x)+a(0.25+x)*a(0.25-x)+a(0.375+x)*a(0.125-x)=0                                                       (28) ##EQU5## for [0</=x</=0.125] 0≦x<0.125.

If a window function a(x) is found which fulfills the above threeconditions, then the synthesis window can be calculated via the systemof equations (30): ##EQU6##

The solutions for the calculation of analysis and synthesis windows ofthe various block overlaps, given in the preceding sections, exhibit asystematic construction. This can be clearly recognized in the matrixequations (18) and, the conditions which the analysis window functionmust fulfill bring, with increasing overlapping, greater restrictionsfor a sensible window design.

For the uniform comparison of the various block overlaps, a Kaiserwindow was selected as the basis. The Kaiser window was modified so thatit satisfies the respective conditions for the overlappingtransformation. This always happened through an expansion correspondingto the window conditions upon pre-determination of the Kaiser windowfunction in a partial region of the window. In the case of the doubleoverlap, the degrees of freedom for the analysis window are so largestill that a complete Kaiser window can be selected here (FIG. 17). Inthe case of the quadruple overlap, the Kaiser window must be modifiedowing to the restricted degrees of freedom as described by equations(16) and (17). With the window construction in FIG. 18, a Kaiser windowwas pre-determined between the standardized time values x=1/8 and x=7/8and the remaining window parts jointed on via the equations (16) and(17). As with increasing overlapping the restrictions for the analysiswindow become larger and larger, the Kaiser window can, in the case ofthe eightfold overlap (FIG. 19), only be pre-determined between x=1/4and x=3/4. The remaining window parts must then be calculated by meansof equations (27) through (29).

FIGS. 17 through 22 show the temporal progression of the window functionand the amount of the Fourier spectrum. The windows are so designed thatthe effective width of the window, i.e., the width of the window inwhich almost the entire energy of the window lies, is the same for alloverlap sizes. This window width corresponds to the window width of thedouble overlap. The nominal window width doubles for every doubling ofthe overlap, as shown in FIGS. 17 through 19.

By choosing the Kaiser window as the analysis window function, thecorresponding synthesis windows receive a camber greater than one. Thisbehavior must be considered when optimizing the windows on the basis ofthe respective application because, if applicable, disturbingcomponents, which ensue upon coding the spectrum, can be slightlyincreased through this If all three time functions of the analysiswindow are compared with each other, then the almost identicalprogression in the region of the effective window width can be clearlyseen. From this there results, in the spectrum, an identical width forthe "main slope" of the amount progression for the Fourier transformedvariable of the analysis window function. In FIGS. 20 through 22, theinfluence which the multiple overlap has on the chosen example can beclearly recognized. Ever smaller window edge values results from therespective doubling of the overlap and the lengthening of the originalKaiser window connected with this. Through this effect there results, inthe spectrum, even greater attenuation into which the spectralprogression grades after the "main slope". The window family should onlybe regarded as an example for the way of operation of the multipleoverlap. The window design must be matched to the respective applicationcase. This means, for example, for an analysis window for the eightfoldoverlap, that through appropriate design the "main slope" becomesnarrower if not such a large attenuation is required after the "mainslope".

FIG. 23 shows the amplitude plot of the spectral lines of a short-timefrequency spectrum, as obtained at the output of state 5 in FIG. 1. Thewhole frequency band of the short-time spectrum f1-f15 is subdividedinto a plurality of frequency groups f1-f2, f2-f4, f4-f12, f12-f14 andf14-f15. In the individual frequency groups, the spectral lines areexamined and weighted according to psychacoustic principles. Only thedominant amplitude values are transmitted, irrelevant amplitude valuesare weighted less strongly or suppressed. The absolute maximum 15 of thewhole frequency band is first transmitted as an absolute value with12-16 bits. The maxima 14, 16, 17, 18 of the remaining frequency groupsare transmitted with an accuracy of 8 bits, i.e., in their relativeposition to absolute maximum 15. The remaining values 20-26 of thefrequency group f4-f12 are related to maximum value 16, i.e. theirdeviation from maximum value 16 is transmitted. To this end theamplitude range is starting from maximum 16, subdivided into threeranges A1, A2, A3 each of 10 dB and one range A4 for the remainder.Signal values 16, 20, 21 or 22, 23 or 24 or 25, 26, lying in each casein an amplitude range are transmitted as an identical value. Nodistinction is therefore drawn between values 16, 20, 21 and 22, 23 and25, 26. The amplitude values 25, 26 at frequencies f10, f11 which fallbelow the value of 30 dB below maximum 16, are set at zero. The phase ofvalues 25, 26 is not transmitted. These spectral components would,because of their close position to value 16 and their small amplitude,in any case no longer be detectable by virtue of the masking effect. Inpractice, the whole frequency band f1-f15 is divided into 26 frequencygroups, of which only 5 are shown in FIG. 23 for the sake of simplicity.Due to dividing into amplitude ranges A1, A2, A3, A4, a total of 2 bitsis sufficient for the transmission of amplitude values 20-26 relative tomaximum 16. For each transmitted amplitude value which lies in theranges A1 to A3, 2 bits are transmitted for the associated phase value.

A considerable reduction in the amount of data required for transmissionis already achieved by the coarse quantization of the amplitude andphase values with 2 bits. An additional saving of bits is also madeduring transmission by dropping components, namely the phase values foramplitude values 25, 26 in frequency group f4-f12. The liberated bitsmay be used for the transmission of a more detailed amplitudesubdivision in ranges A1-A3. To this end, for example, each range A1-A3is divided into two ranges of 5 dB each. Moreover, there is assigned toeach frequency value 20-24 a bit which indicates whether the amplitudevalue, e.g. 20, 21, lies within the first 5 dB or the second 5 dB belowmaximum 16. The assignment of these bits takes place on the basis of atable 28 which is created at the transmitter and is reconstructable at areceiver. To this end there is placed over the whole plot of thefrequency spectrum in FIG. 23 a grid 27 with gradation in stages of 6dB. Amplitude values 20-24 are therefore assigned to this grid. Table 28assigns to each amplitude value 20-24 a particular position in relationto maximum 16. Table 28 begins with the lowest frequency value and showsby means of the line the respective position in relation to the maximumof the corresponding frequency range.

If further free bits are available, a subdivision of the 5 dB rangesinto 2.5 dB ranges will be carried out. The subdivision process may becontinued indefinitely. The saving of bits and the use of these bits forrefinement of resolution is termed adaptive quantization.

FIG. 24A shows the pre-processing of a sudden acoustic event waveform 29which occurs within a time window t1-t7 at a point in time t9. Such anacoustic event may be e.g. the striking of a musical instrument such asa triangle. The pre-processing takes place prior to step 5 frequencytransformation. Acoustic event 29 is also preceded by a preshoot betweent8 and t9, which is inaudible due to a preliminary masking. Duringconversion into the frequency spectrum in stage 5 in FIG. 1 there arisesin each case in the frequency domain a signal which indicates thespectral distribution in window t1-t7. Since in the case of said signalthe assignment of spectral lines to individual points in time within atime window no longer takes place, event 29 averaged over the whole timewindow t1-t9 would therefore seem to be blurred. An audible distortionmay occur as a result.

In order to prevent this possible defect, a time window t1-t7 or blockis subdivided into 32 sub-blocks as shown in FIG. 24B. The amplitudes ofthe individual sub-blocks are determined. As soon as an amplitudeincrease of more than 20 dB occurs between two sub-blocks, produced inFIG. 24 by event 29, an additional measure will be triggered as shown inFIG. 24C. This measure consists in the fact that prior to the amplitudeincrease the signal is by means of a companding process, increased atthe transmitter and correspondingly reduced again at the receiver. Theabove-mentioned defects caused by the blurring of the short-time eventover the whole time window will thereby be reduced.

We claim:
 1. A signal transmission method in which an analog signal is converted into a digital signal, transmitted in digital form and reconverted into an analog signal and whereby said digital signal is partitioned by means of overlapping time windows in temporally successive blocks which are each converted into a signal sequence representing a short-time spectrum, said method comprising the steps ofa) windowing said digital signal and forming temporal blocks of block length TB with overlapping regions of relative size N-1/N where N=[2 to the power of n] 2^(n) for whole numbers of n, whereby overlapping blocks are selected each having a fixed number of samples; b) transforming said samples of each block by subjecting individual ones of said blocks offset by TB/2*N in the time domain to a sine or cosine transformation respectively to produce transform output values; c) sampling said transform output values at different positions, causing aliasing, said sampling comprising sampling said transform output values from N consecutive values according to a sampling scheme: C1: 0, N, 2N, 3N . . . , or a subsampling scheme C2: N/2, 3N/2 [/ whereby four combinations with respect to transformation and sub-scanning forms result:] resulting in four combinations oftransformation and sampling forms K1-K4 as followsK1: cosine transformation+selection scheme C1 K2: cosine transformation+selection scheme C2 K3: sine transformation+selection scheme C1 K4: sine transformation+selection scheme C2; d) arranging sampled transform output values so that said aliasing arises at predetermined positions, by applying one of said combinations K1 . . . K4 in any arbitrary permutation on each of overlapping blocks, whereby four groups of values with entries for overlapping regions of blocks results, said groups of values being differentiated by their preceding signs; e) said arranging including selecting a combination from K1 . . . K4 so that after inverse transformation at a receiver and summation of the components in the signal segments of the blocks involved in the overlap, all signals not originating from the same segment of the original signal are compensated whereby said aliasing is cancelled in a receiver; f) coding, transmission and decoding said sampled/sub-sampled transform output values of individual blocks after said arranging; g) subjecting decoded individual blocks to inverse sine or cosine transformation, producing inverse transform values; h) arranging said inverse transform values so that non-aliased components corresponding to original input blocks are located in respective original positions, said arranging of said inverse transform values including segmentation of continuous-time inverse transform signal values into successive signal segments Ni for i=1, 2, 3 . . . , which, depending on the combination K1 . . . K4 used, contain components Ni . . . and temporally reflected alias components Si . . . ; and i) summing said signal segment components Ni . . . and said temporally reflected alias components Si . . . in the signal segments Ni of overlapping blocks.
 2. A method according to claim 1, wherein:a. said blocks are evaluated using analysis windows prior to transformation and synthesis windows after transformation, and said windows form segments of length TB/N equal to said signal segments; b. said evaluation is performed by multiplying said signal components Ni . . . or, respectively, said temporally reflected components Si . . . corresponding to said signal components by components of analysis window ani . . . or, respectively, temporally reflected components asi . . . corresponding to these components and components of synthesis window sni . . . ; and c. said analysis and synthesis windows fulfill the following conditions in block overlap regions:I. the sum of temporal regular wanted signal components of an analysis window and synthesis window superimposed in signal segments of a block is equal to one; II. the sum of temporal regular aliasing components of an analysis window and synthesis window superimposed in signal segments of a block is equal to zero,
 3. A method according to claim 2, wherein with said windows symmetric about a block center and with double overlapping, a synthesis window function is determined from a pre-determined analysis window function according to the following equation: ##EQU7## for [0 less or x less or 0.5] 0≦x≦0.5 where s(x) is a synthesis window function,a(x) is an analysis window function, x represents a standardized time with a value of 0 at the start of a block and a value of 1 at the end of said block.
 4. A method according to claim 2, wherein with said windows symmetric about a block center and with quadruple overlapping, an analysis window function is first determined which fulfills the following equations:

    a(0.5-x)*a(x)=a(0.25-x)*a(0.25-x)

    a(1-x)*a(x-0.5)=a(0.75-x)*a(0.75-x)

for 0≦x≦0.25 where a(x) is an analysis window function, and a synthesis window function is determined from a previously determined analysis window function according to the following equation: ##EQU8## where sni are components of a synthesis window function, ani are components of an analysis window function, x represents a standardized time with a value of 0 at the start of a block and a value of 1 at the end of said block.
 5. A method according to claim 2, wherein with said windows symmetric about a block center and with eightfold overlapping, an analysis window function is first determined which fulfills the following equations:

    a(x)*(0.25-x)=a(0.125)+x)*a(0.125)-x)

    a(x)*a(0.5-x)+a(0.125+x)*a(0.375-x)+a(0.25+x)*a(0.25-x)+a(0.375-x)*a(0.125-x)=0 ##EQU9## for 0≦x≦0.125 where a(x) is an analysis window function, and a synthesis window function is determined from a previously determined analysis window function according to the following system of equations: ##EQU10## where sni are components of a synthesis window function, ani are components of an analysis window function, x represents a standardized time with a value of 0 at the start of a block and a value of 1 at the end of said block. 